Astrofísica e Tecnologia Aeroespacial

On the Need for Correction of Newton′s Law of Universal Gravity within Classical Physics

Abstract

Valentyn Nastasenko

Newton's law of universal gravitation was discovered by him, perhaps in 1679, and published in 1687 in his paper “Principia”. At the beginning, he simply established a correspondence between the gravitational force F and the masses m₁ and m₂ of 2 point objects located at a distance r between them: F ~ m₁m₂/r². However, this dependence is not a strict physical law, since the numerical value of the gravitational force found from it is not its real value. Therefore, instead of similarity, a transition coefficient should be introduced. It was first determined experimentally by Cavendish in 1798. Further, this coefficient was presented as the gravitational constant G. However, Cavendish did not connect G with Newton's dependence, but used it only to calculate the Earth's mass M within the framework of the GM combination. The constant G from this combination was identified by Jolly in 1878, which reduced Newton's original dependence to the real law of universal gravitation F=Gm₁m₂/r², which is currently used. However, Newton got his dependence on the basis of the rotation of the Moon around the Earth, whose orbit is close to circular. Therefore, the radius r in it was taken constant. This law is being criticized because it does not operate at the planetary level, where the planets of the solar system do not move in a circular orbit, but, elliptical, within the framework of Kepler's laws. Eliminating the discrepancy between Newton's law of universal gravitation and Kepler's laws is the goal main of this work, and the formulation of a new corrected law is its scientific novelty. As a result of this work, it was proposed to replace the radius r with the current value r_i in Newton's law, which can change according to its own laws. In this case, the new value of the law of universal gravitation has the form: F=Gm₁m₂/r_i². Unlike the original Newton's law, in which the radius r=const, in the corrected law r_i=var, so the original law is a special case of the corrected law. In this case, the value of the radius r_i² can be obtained through the coordinate’s x_i², y_i² of the current points of the trajectory of the center of mass m₂ of an object of smaller magnitude relative to the center of mass m₁ of an object of larger magnitude. For an object with a spatial form of the trajectory of the center of mass, the 3^rd coordinate z_i² is added to determine this radius. In its final form, the new law of universal gravitation will be expressed by the dependence: F=Gm₁m₂/(x_i²+y_i²+z_i²). Thus, despite the criticism of Newton's law by opponents, he is acted, acts and will act in the material world. Conclusion, the Proposed revised law of universal gravitation are recommended for use in scientific research. This corrected version should be included in all textbooks and reference books on physics, incl. in the encyclopaedia.